Abstract
This study investigates the hypothesis that there is a natural number bias that influences how students understand the effects of arithmetical operations involving both Arabic numerals and numbers that are represented by symbols for missing numbers. It also investigates whether this bias correlates with other aspects of students’ understanding of the number concept beyond natural numbers. Natural number bias has been characterized as the interference of natural number knowledge in reasoning about non-natural numbers. Quantitative data is presented showing that in the case of operations between numbers and missing numbers this bias acts in two main ways. First, it shapes students’ anticipations about the expected outcome of each operation, that is, that the result of addition or multiplication “must” be bigger than the initial numbers and the result of subtraction or division “must” be smaller. Second, it causes students to think that missing numbers stand mostly for natural numbers; this tendency would lead students to make decisions about the general results of operations by substituting only natural numbers for the missing number symbols. It is argued that knowledge about operations between natural numbers needs to be inhibited for students to overcome the natural number bias and to reason with numbers beyond the scope of natural numbers.
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